Decompositions of Ordered Semigroups into a Chain of k-Archimedean Ordered Semigroups

Abstract

In this paper, we rst dene various types of k-regularity of ordered semigroups and various types of k-Archimedness of ordered semigroups. Also, we dene the relations T(k); T(k)l ; T(k)r ; T(k)t and T(k)b (k in Z+) of on an ordered semigroup. Using these notions, lter, and the radical subsets of ideal, left ideal and bi-ideal of ordered semigroups we describe chains of k-archimedean (left k-archimedean, t-k-archimedean) ordered subsemigroups.
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